The measure defined above has the following properties:

1. i)

   $c_{1}(\mathfrak{L}_{1})\wedge...\wedge c_{1}(\mathfrak{L}_{n})$ is a discrete measure (i.e. of the form $\sum_{x\in S}\lambda_{x}\delta_{x}$ with $S\subseteq X$ a closed discrete subset, $\lambda_{x}\in\mathbb{R}$ and $\delta_{x}$ the Dirac-measure at $x$) whose support is contained in the relative interior of $X$ over $K$ (in the sense of [Ber93, 1.5]).

2. ii)

   $c_{1}(\mathfrak{L}_{1})\wedge...\wedge c_{1}(\mathfrak{L}_{n})$ is multilinear and symmetric in $\mathfrak{L}_{1},...,\mathfrak{L}_{n}$.

3. iii)

   Let $\varphi:\mathfrak{X}^{\prime}\rightarrow\mathfrak{X}$ be a proper morphism of admissible formal schemes over $K^{\circ}$ with irreducible and reduced generic fibres of dimension $n$ such that the induced morphism on the generic fibres is surjective. Then for formal line bundles $\mathfrak{L}_{1},...,\mathfrak{L}_{n}$ on $\mathfrak{X}$ we have

   $$(\varphi^{\textup{an}})_{\ast}\left(c_{1}(\varphi^{\ast}\mathfrak{L}_{1})\wedge...\wedge c_{1}(\varphi^{\ast}\mathfrak{L}_{n})\right)=\Deg(\varphi^{\textup{an}})c_{1}(\mathfrak{L}_{1})\wedge...\wedge c_{1}(\mathfrak{L}_{n}).$$